Chen, Qiuhui Dang, Pei Qian, Tao
Published in
Science China Mathematics

We use the Weyl correspondence approach to investigate the spectral operators of the Laguerre and the Kautz systems. We show that the basic functions in the Laguerre and the Kautz systems are the eigenvectors of modified Sturm-Liouville operators. The results are further generalized to multiple parameters of one complex variable in both the unit di...

Gao, Yan Zeng, Jinsong
Published in
Science China Mathematics

Based on the distortion theory developed by Cui and Tan (2015), we prove the landing of every parameter ray at critical portraits coming from non-recurrent polynomials, thereby generalizing a result of Kiwi (2005).

Lacave, Christophe Wang, Chao
Published in
Science China Mathematics

For equations of order two with the Dirichlet boundary condition, as the Laplace problem, the Stokes and the Navier-Stokes systems, perforated domains were only studied when the distance between the holes dε is equal to or much larger than the size of the holes ε. Such a diluted porous medium is interesting because it contains some cases where we h...

Kammerer, Clotilde Fermanian Fischer, Véronique
Published in
Science China Mathematics

In this paper, we develop semi-classical analysis on H-type groups. We define semi-classical pseudodi fferential operators, prove the boundedness of their action on square integrable functions and develop a symbolic calculus. Then, we define the semi-classical measures of bounded families of square integrable functions which consist of a pair forme...

Cao, Wentao Székelyhidi, László Jr.
Published in
Science China Mathematics

In this short note we revisit the convex integration approach to constructing very weak solutions to the 2D Monge-Ampére equation with Hölder-continuous first derivatives of exponent β

Sueur, Franck
Published in
Science China Mathematics

In this survey we report some recent results on the dynamics of a rigid body immersed in a two-dimensional incompressible perfect fluid, with an emphasis on the zero-radius limit.

Monniaux, Sylvie
Published in
Science China Mathematics

Depending on the geometry of the domain, one can define—at least—three different Stokes operators with Dirichlet boundary conditions. We describe how the resolvents of these Stokes operators converge with respect to a converging sequence of domains.

Ifrim, Mihaela Tataru, Daniel
Published in
Science China Mathematics

This article is concerned with infinite depth gravity water waves in two space dimensions. We consider this system expressed in position-velocity potential holomorphic coordinates. Our goal is to study this problem with small wave packet data, and to show that this is well approximated by the cubic nonlinear Schrödinger equation (NLS) on the natura...

Paicu, Marius Zhang, Ping
Published in
Science China Mathematics

We consider three-dimensional incompressible Navier-Stokes equations (NS) with different viscous coefficients in the vertical and horizontal variables. In particular, when one of these viscous coefficients is large enough compared with the initial data, we prove the global well-posedness of this system. In fact, we obtain the existence of a global ...

Baldi, Annalisa Franchi, Bruno Pansu, Pierre
Published in
Science China Mathematics

In this paper, we prove Poincaré and Sobolev inequalities for differential forms in L1(ℝn). The singular integral estimates that it is possible to use for Lp, p > 1, are replaced here with inequalities which go back to Bourgain and Brezis (2007).